Thin-walled Steel Members Research Articles

On the required ductility in beams and connections to allow a redistribution of moments in steel frame structures

The structural behaviour of beam-column joints plays a critical role in the seismic response of frame structures. In the case of steel rack systems, uprights (columns) are usually 3rd or 4th class open thin-walled cold-formed steel members according to Eurocode 3, as such, local buckling occurs before the plastic moment resistance (in the case of the 3rd class) or yield stress (4th class) is achieved. Beams are usually 1st or 2nd class, so they can form a plastic hinge with the rotation capacity required from plastic analysis without reduction of the resistance (1st class) or with a limitation on the rotation capacity due to local buckling (2nd class). For this reason, only beams and connections, which can be easily equipped with additional bolts to increase their structural performance, can provide a post-elastic behaviour with energy dissipation. This paper presents and develops a method capable of evaluating the rotational capacity, or ductility, required by beams and connections to perform a plastic design. The proposed approach allows for the failure mode of the structure to be predicted starting from mechanical properties of structural members, and it is valid for both service and seismic loads. The analytical method could be applied to different structural systems and materials; in the present work it is presented with reference to industrial pallet racks. Theoretical assessment herein of the required plastic rotation for beams and connections provides useful information for bolted connection design to increase capacity of the racks with minimal additional cost.

Evaluation of rack connection mechanical properties by means of the Component Method

Steel storage pallet racks are characterised by the extensive use of thin-walled cold-formed steel members and boltless beam-column connections, whose structural behavior plays a key role in the seismic response of rack systems. Due to the great variety of connector types and member geometries, the current design codes require experimental tests on rack connections to obtain their mechanical characteristics. The drawback is that these experimental procedures are expensive and time-consuming.In this paper a theoretical mechanical model, based on the application of the Component Method (CM), is proposed with the aim to assess the flexural resistance and initial elastic stiffness of rack connections. Results are compared with experimental data collected in an experimental campaign carried out on several full-scale joints, belonging to different types produced by the same manufacturing company.The comparison highlights the accuracy of the proposed model that permits the weakest component of the joint and its failure mode to be evaluated. The CM provides fundamental information about the influence of structural details on the joint behavior, and it could be used in the design of rack connections to improve their structural response. The proposed mechanical model appears appropriate for predicting features of studied connections and especially for analyzing main components, which influence the initial rotational stiffness and the ultimate bending moment of rack connections. Finally the proposed model can be easily modified to be used in the analysis of other connector types, as only a limited number of structural and geometrical data are required for its definition.

Vibration behavior of thin-walled steel members subjected to uniform bending

Abstract This article reports the results of an investigation on the effects of internal moments on the vibration behavior of thin-walled steel members. The analyses are based on the Generalized Beam Theory (GBT), a thin-walled bar theory accounting for cross-section in-plane deformations - its main distinctive feature is the representation of the member deformed configuration by means of a linear combination of cross-section deformation modes, multiplied by their longitudinal amplitude functions. The study concerns a simply supported T-section (with unequal flanges) members exhibiting a wide range of lengths and subjected to uniform internal moment diagrams - their magnitudes are specified as percentages of the corresponding critical buckling values. After providing a brief overview of the main concepts and procedures involved in performing a GBT-based structural analysis, the vibration behavior of load-free and loaded T-section members is addressed - the influence of the applied loadings is assessed in terms of (i) the fundamental frequency difference and (ii) the change in the corresponding vibration mode shape. For validation purposes, some GBT results are compared with values yielded by shell finite element analysis performed in the code ABAQUS (Simulia, 2008).

A modified ECBL approach for cold-formed steel rack section members

The calibration of appropriate buckling curves for interactive local/distortional-global buckling of thin-walled cold-formed steel members is a task well covered by the Erosion of Critical Bifurcation Load (ECBL) approach. In this context, here a modified formulation of the ECBL approach, based on a new definition of the mode interaction point, is presented. The Generalized Beam Theory is used to find the mode interaction points and the related imperfections. Pallet rack uprights in compression are studied to show the potentialities of the modified ECBL approach and mark the differences with the classical one. The buckling curves coming from the modified ECBL approach are also compared with experimental results and with the buckling curves evaluated following the EN15512:2009.

Design Reliability Analysis of Cold-Formed Thin-Walled Steel Members with Lipped Channel Sections Considering Distortional Buckling

Introduction: Based on the experimental results of cold-formed thin-walled steel lipped channel sections, the uncertainty of calculating mode of load-carrying capacity using effective width method considering distortional buckling for different material types cold-formed steel compressed members was researched, and the uncertainties of material strength and geometric characteristics of the typical sections were statistically analyzed. Methods: According to the recommended resistance of partial coefficient in the draft of Technical code of cold-formed steel structures (GB50018-), the reliability indexes of cold-formed thin-walled steel lipped channel sections under compression were investigated using the improved first-order second-moment method considering different possible external loading combinations. Results: The analyzed results show that, using the recommended resistance partial coefficient in the code draft, the reliability indexes of the compressed members with width-thickness ratio within the limitation of code draft can well met the target reliability index. The suitability of the corresponding calculating modes of load-carrying capacity considering distortional buckling was established.

Experimental and numerical investigation on the non-uniform temperature distribution of thin-walled steel members under solar radiation

The temperature effect often significantly affects the performance of large-span spatial structure and even becomes one of the controlling loads. To obtain the non-uniform temperature field distribution of the thin-walled steel members under solar radiation and the influence rules of various factors, in this paper, experimental studies are carried out with three groups of specimens including rectangular steel tube, I-shaped steel and circular steel tube. Based on the test data, the non-uniform temperature field distributions considering the influence of solar radiation intensity, member size and surface coating are analyzed in detail. Then, numerical methods for the temperature field of steel members are studied considering multiple environmental factors. The validity of the numerical method is evaluated with test results. Finally, based on the parametrical studies of the major influence factors, a simplified calculation approach is presented for practical engineering applications. The experimental study demonstrates that the non-uniform temperature distribution of steel members truly exists and cannot be overlooked. The numerical method for the temperature field in this paper is effective, and the simplified calculation approach can meet the required engineering precision. The research methods and conclusions of this work can provide valuable references for thermal design, monitoring and control of steel structures.

Monotonic and cyclic tests on beam-column joints of industrial pallet racks

Pallet racks are characterized by boltless beam-column connections and the extensive use of thin-walled cold-formed steel members. Due to the great number of beam-end connector types and member geometries, a reliable evaluation of their structural behavior, especially under seismic loads, requires a thorough modeling of beam-column joints, whose moment-rotation curves can be reliably assessed only through experimental tests. In this paper, the authors present results of monotonic and cyclic tests on four different types of industrial rack joints. Tested joints differ from one another in the type of beam-connector, which is obtained by folding the beam end or is welded to the beam-end section with different welding layouts. Moreover, joints differ in the number of tabs and the relative thickness of the upright and the beam-end connector. Experimental results from cyclic tests allows for moment-rotation curves of joints to be accurately identified, confirming that they are significantly different from traditional steel framed buildings due to pinching in hysteresis loops. Obtained curves can be used for reliable modeling of joints in seismic analyses of steel pallet racks. As producers of steel rack structures are interested in reducing the total welding length of beam-end connectors for time efficiency and cost saving, the influence of the welding layout of beam-end connectors on the structural response and failure mode of joints has also been investigated. Finally, some joints have also been equipped with additional bolts to evaluate their influence on the bearing capacity, initial elastic stiffness and dissipated energy per cycle.

Stochastically simulated mode interactions of thin-walled cold-formed steel members using modal identification

The purpose of this paper is to investigate the impact of the geometric imperfection on the interaction of buckling modes for thin-walled cold-formed steel members with a quantitative modal identification approach. Previous studies showed that the interaction of buckling modes varies during the loading process and how buckling interacts depends not only on the section itself but also on the geometric imperfections in the member. This interaction could change the failure modes of the member and its strength accordingly. This paper integrates a modal identification approach based on constrained finite strip method to track this interaction out of the shell finite element model for nonlinear collapse analyses. The geometric imperfections are included in the computational shell finite element model using the traditional modal approach with stochastically simulated magnitudes. The simulations are performed on five specially selected cold-formed steel sections that are deemed to be local-dominant, distortional-dominant, local-distortional interacted, Pcr-equal interacted, and Pn-equal interacted. The deformations of the analyses are categorized into the fundamental deformation modes commonly available to cold-formed members: local, distortional, and global. Sensitivity of imperfection is studied by tracing the variation of mode interaction, in particular, for the failure mode. Peak load and associated mode participations are investigated. In addition, a statistical study of the impact of imperfections on the potential failure mode at peak is provided. The potential correlation of the member strength with mode participation is explored, which will shed light on the coupled instability of cold-formed steel member, in particular on investigating the impact of mode participations to member strength.

Plastic mechanisms of thin-walled cold-formed steel members in eccentric compression

The paper investigates the possibility to use the local plastic mechanisms to characterise the ultimate strength of short thin-walled cold-formed steel members subjected to eccentric compression about the minor axis. The research is based on previous studies and some new investigations of the authors. The plastic mechanisms for lipped channel members in eccentric compression about minor axis and the evolution of those mechanisms are analysed. Five different types of mechanisms for members in compression with different eccentricities are examined.

Experimental Investigation of Compressed Thin-Walled Steel Members

The paper presents fundamental information about realized experimental-theoretical research to determinate the load-carrying capacities for thin-walled compressed steel members with quasi-homogenous and hybrid cross-sections. The webs of such members are stressed in the elastic-plastic region. This continuous research joins on previous research of the first author of the paper. The aim of this research is to investigate and analyse the elastic-plastic post-critical behaviour of thin web and its interaction with flanges. The experimental program, test members and their geometrical parameters and material properties are evident from table 1 and table 2 as well as from figure 1 and figure 2. The test arrangement and failures of the test members are illustrated on Figures 3, 4 and 5. Some partial results are presented in Table 3 of the paper, too.

Behavior of thin-walled circular hollow section stub columns under axial compression

Thin-walled steel circular hollow section (CHS) is widely used in wind turbine towers, where the tube is subjected to axial load combined with bending moment. Understanding the behavior of axially loaded thin-walled tubes with large diameter-to-thickness (D/t) ratios is crucial for the design of such structures. To investigate the behavior of axially loaded thin-walled circular hollow section steel tubes, 16 stub columns were tested with the D/t ratio ranging from 75 to 300. The experimental results showed that the compressive strength decreased sharply with the increase of the D/t ratio. The experimental result indicated that the tubes with smaller D/t ratios failed with outward deformation without visible local buckling. With the increase of the D/t ratio, local buckling appeared at the peak load. The finite element method was used to model the behavior of axially loaded stub columns. The experimental results were used to validate the accuracy of the finite element results. Based on the finite element model, the influences of the D/t ratio, the initial geometric deformation and the initial residual stress were analyzed. Design guidelines in Eurocode3, AISC-LRFD, AS4100 and S16-9 on thin-walled steel members were used to compare with the experimental and calculated results. Among them, the results based on AS4100 were the closest to the experimental results.

Evaluation of the erosion of critical buckling load of cold-formed steel members in compression based on Koiter asymptotic analysis

An imperfection sensitivity analysis of thin-walled cold-formed steel members in compression is presented. The members under investigation are perforated steel pallet racks in compression of different lengths. The analysis is based on a finite element implementation of the Koiter method coupled with Monte Carlo simulation. It is based on an intensive experimental study carried out at the Politehnica University of Timisoara, which showed a strong interaction of the buckling mode with a significant reduction in the load carry capacity. Using Koiter's method the limit load is evaluated statistically analysing thousands of geometrical imperfections. Based on this, the worst combination of imperfections is detected and the erosion of the critical buckling load due to imperfections and modal interaction, is evaluated. A critical discussion of the results is presented with reference to some aspects of Koiter's analysis and how to use these in subsequent GMNIA analysis to account for the nonlinear effects of the material due to plasticity.

In-Plane Behavior of Timber-Steel Hybrid Floor Diaphragms: Experimental Testing and Numerical Simulation

This paper presents the results of experimental and numerical studies on the in-plane behavior of a novel timber-steel hybrid floor diaphragm. The proposed diaphragm system consists of C-shaped thin-walled steel members that are used as joists and dimension lumber that is placed on top of the joists to form a timber decking. The dimension lumber is further connected to the steel joists by screws. In-plane loading tests were conducted to investigate the failure modes, in-plane load resisting capacity, stiffness degradation, and energy dissipation of the proposed hybrid diaphragm. In terms of deformation characteristic, results showed that shear deformations contributed up to 90% of the total in-plane deformation of the hybrid diaphragm. The load resisting behavior of the diaphragm showed an obvious nonlinear characteristic with stiffness degradation, and the ductility of the diaphragm was found to be closely related to the failure mode of the screwed connections between the steel joists and the timber decking. A nonlinear finite element model of the hybrid diaphragm was then developed and verified using the test results. A specific feature of the numerical model was the introduction of the user defined element HYST spring to simulate the hysteretic behavior of screwed wood-steel connections. Results showed that the numerical predictions agreed reasonably well with test results in terms of hysteresis loops, stiffness degradation, and energy dissipation. The proposed numerical model, which is capable of predicting the nonlinear behavior of the diaphragm, can further serve as a useful tool for the evaluation of the mechanical behavior of the proposed diaphragm under more realistic and complicated loading scenarios. The experimental and numerical results presented in this study represent a basis of knowledge for the further development and application of such a timber-steel hybrid diaphragm.

Plastic Mechanisms for Thin-Walled Cold-Formed Steel Members in Eccentric Compression

Abstract The Eurocode 3 concerning thin-walled steel members divides members subjected to compression into four classes, considering their ductility. The representatives of the class C4 are short bars, for which the load-capacity corresponds to the maximum compression stresses less than the yield stress. There are bars prone to local buckling in the elastic range and they do not have a real post-elastic capacity. The failure at ultimate stage of such members, either in compression or bending, always occurs by forming a local plastic mechanism. This fact suggests the possibility to use the local plastic mechanism to characterise the ultimate strength of such members. The present paper is based on previous studies and some latest investigations of the authors, as well as the literature collected data. It represents an attempt to study the plastic mechanisms for members in eccentric compression about minor axis and the evolution of plastic mechanisms, considering several types of lipped channel sections.

Cyclic flexural response and energy dissipation of cold-formed steel framing members

This manuscript summarizes an experimental program investigating the cyclic flexural behavior and energy dissipation of C-shaped cold-formed steel structural framing members experiencing global, distortional or local buckling. Understanding the cyclic flexural moment-rotation (M–θ) response of individual members is essential in developing analytical models that can facilitate analysis-based design of cold-formed steel building systems. Specimen cross-section dimensions and lengths were selected to isolate specific buckling modes (i.e., local, distortional or global buckling). A cyclic loading protocol was adapted from FEMA 461 with targets based on elastic buckling properties. Abrupt drops in flexural strength after peak moment were observed with subsequent stiffness degradation and pinching of the moment-rotation response associated with straightening of buckling deformations during loading direction reversals. Members experiencing local and distortional buckling accumulated damage at the compressed web and flanges within the leading buckled half-wave that spread throughout the cross-section forming flexural hinges after several cycles. In members experiencing lateral-torsional buckling, damage localized at the C-section flange-stiffening lip but distinct flexural hinges were not observed. Energy dissipation per cycle in members undergoing lateral-torsional buckling remained constant through large flexural rotations because the failure mechanism involved mid-span cross-section rigid body motion without plastic deformations spreading across the cross section. Local and distortional buckling specimens resulted in more dissipated energy per cycle compared to global buckling specimens, but the energy dissipation rapidly decreased as applied displacements increased. Energy dissipation within the damaged half-wave(s) is higher for lower cross-sectional slenderness and increasing section modulus, key trends that will be useful for generally defining cyclic hysteretic response of thin-walled cold-formed steel members in planned future work.

Beam design for steel storage racks

Thin-walled cold-formed steel members are used worldwide in industrial systems for the storage of goods and materials, such as drive-in, drive-through and selective pallet racks. A relevant difference with respect to the more traditional civil and industrial steel structures consists in the extensive use of thin-walled cold-formed members having non-bisymmetric cross-sections. This choice allows for the best possible structural performance while minimizing weight, and hence, achieving a very low cost of the skeleton frames. The design is influenced by the typical problems associated with the use of slender cross-section members and by the warping effects. Therefore, design of these industrial structures appears quite complex, because in engineering offices the most commonly used finite element (FE) software analysis packages offer beam formulations that are only capable of modeling the behavior of members having two axes of symmetry.The paper deals with the design of beams used in industrial storage systems. Refined parametric analyses have been carried out by means of an open source FE software package able to simulate the behavior of non-symmetric cross-section members. With reference to lipped channel and zed beams, the contribution of warping effects has been investigated with regard to not only the in-service displacements and rotations, but also focusing on its influence in the distribution of stresses at the ultimate limit state. Furthermore, in order to investigate the differences associated with the use of 6DOF and 7DOF FE beam formulations, Appendix A proposes two design examples, which are also reproduced in Appendix B by hand calculations.

European and United States approaches for steel storage pallet rack design: Part 1: Discussions and general comparisons

A very common application of cold-formed thin-walled steel members regards the industrial storage systems for goods and products, such as pallet racks, which are the core of the present paper. Owing to the increasing needs associated with globalization as well as the importance of the logistics, nowadays, rack manufactures must be highly competitive in the most industrialized countries: as a consequence, it is frequently required that engineers design in accordance with standards of the country where the storage rack will be in service. Due to peculiarities associated with the requirements of each code, different values of the rack load carrying capacity are expected and their quantification should be of great interest for commercial reasons: this is an important open question for designers and manufactures that up to now is without any practical response.A two-part paper has been written to summarize the main results of a comparative study on pallet rack design provisions currently adopted in Europe and the United States. Part 1 describes the key features of both codes, discussing similarities and differences associated with the admitted design procedures with reference to the member verification procedures and to the alternative analysis approaches. Furthermore, practical comparisons related to isolated members under compression and bending are proposed to allow a direct appraisal of structural performance.The companion paper (part 2: Practical applications) reports on an exhaustive analysis with regards to the contents herein introduced and applied to the design of 216 medium-rise semi-continuous pallet racks that are unbraced in the longitudinal direction.

Cold-formed steel member bending stiffness prediction

The objective of this paper is to provide a simplified method for predicting the bending stiffness of thin-walled cold-formed steel members subject to elastic (or inelastic) local or distortional buckling. In thin-walled cold-formed steel members for serviceability and consideration of deformations (second-order effects) it is important to account for the loss of cross-section bending stiffness due to the use of slender elements and/or yielding. Although existing design specifications provide some guidance on how to predict the stiffness, limited information is available for cross-sections subject to distortional buckling or undergoing inelastic local and/or distortional buckling. Existing tests and shell finite element analysis on cold-formed steel beams failing in local or distortional buckling are used as the basis for the study conducted herein. Stiffness of the conducted tests and finite element models is compared with predictions based on the Effective Width Method and Direct Strength Method. Relationships between local and distortional cross-section slenderness and the observed and predicted secant stiffness up to the peak load are examined. New design expressions to predict cold-formed steel member bending stiffness depending on cross-section slenderness are presented. The new methods are proposed for adoption in cold-formed steel specifications.

European alternatives to design perforated thin-walled cold-formed beam–columns for steel storage systems

Summary Rack systems to store goods and products are one of the most important applications for thin-walled cold-formed steel members. Adjustable pallet racks are used widely worldwide and are characterized by regular systems of perforations along the uprights (i.e. vertical members) to connect easily pallet beams and diagonal members forming the skeleton frame. Design rules are based on the well-established approaches for the more traditional solid members, suitably extended to account for the presence of regular perforations via component tests accurately described in rack specifications. This paper focuses on the performance of isolated uprights under axial load and gradient moment. In particular, three European alternatives to design beam–column rack members have been discussed and applied: the first and the second are traditionally used for thin-walled cold-formed steel members while the latter, the so-called general method of Eurocode 3 part 1-1, allows to take directly into account the key features associated with upright response. The geometry of the cross-sections and of their perforation system, the member slenderness and the load condition has been assumed as parameters of this study. Research outcomes demonstrate that the predicted performances can result significantly different, reflecting directly on the weight and the cost of the whole storage system. Furthermore, numerical analyses and design calculations show that standard codes need urgent revisions, leading in few cases to design beam–columns from the unsafe side.

Study on Buckling of Two Kinds of Thin-Walled Steel Members with Imperfection

Based on Ježek method of computing the elastic-plastic buckling of the members under the axial compressive load and the bending moment, considering the initial imperfection, the analytical expressions of calculating the ultimate load of buckling about the neutral axis with the maximum moment of inertia for an H-shaped member and a square steel tube member are derived. Using the elastic-plastic finite element method and the theory of nonlinear buckling, the impact by initial geometric imperfections on the H-shaped steel member and the square steel tube member under the axial compressive load and the bending moment are analyzed and the numerical solutions of ultimate bearing capacity are obtained. By compared with the values of the finite element method (FEM), it shows that the analytical method in this paper is valid. The results of the example show that the presence of initial imperfections reduces the ultimate bearing capacity of the two kinds of steel members to a great extent. It is also found that the influence of the initial geometric imperfection on the ultimate bearing capacity of members is smaller when the bending moment increases.